湍流燃烧二阶矩模型的研究进展

湍流燃烧模型在燃烧过程数值模拟中十分重要。商业软件中仍然应用的简单模型,如EBU和预设PDF模型,常常不能很好地模拟有限反应动力学。目前通行的湍流燃烧模型,如层流小火焰模型和条件矩模型,只对一定的火焰类型和火焰结构的效果较好。PDF方程模型更通用,但计算量太大,用于大涡模拟更是如此。另一类是统计矩模型,即基于湍流模型的思路,用雷诺展开和取平均,封闭未知项的二阶矩模型,但是遇到了高度非线性的温度指数函数的困难。不同研究者采取了不同的近似处理,都低估了时平均反应率。作者彻底放弃各种近似方法,构建了终版的二阶矩模型,用于不同的单相和两相燃烧的雷诺平均模拟和大涡模拟,得到了实验验证和直接数值模拟的验证。     

基于Lagrange方法封闭的两相湍流场方程模型

两相湍流场方程模型采用基于Euler方法的一阶矩方程,而二阶矩方程由Lagrange方法得到,新模型的封闭不需要附加其它假设.首先基于概率密度函数给出颗粒运动的连续方程和动量方程,其次由基于平均Langevin方程的Lagrange模型推导得到颗粒二阶矩方程,最终获得封闭的二阶矩模型.将新模型用于气固两相壁面射流的数值模拟,结果表明新模型合理有效.     

四阶精度显式滤波大涡模拟方法研究

在传统大涡模拟方法的基础上引入显式滤波技术,有效地控制了最小解析尺度区域的各种数值误差.对有限差分格式的守恒特性进行了研究,发展了适用于三维平板通道大涡模拟的四阶精度守恒格式.分别利用二阶和四阶精度的传统与显式滤波大涡模拟程序模拟平板通道内的湍流流动,将计算结果与DNS数据进行了对比,得到了合理结果.     

尺度自适应模拟和大涡模拟的关联性分析

采用理论分析和数值模拟相结合的方法,系统研究了尺度自适应模拟（scale-adaptive simulation,SAS）和大涡模拟（large-eddy simulation,LES）的关联性问题.在理论分析方面,对比分析了系综平均和滤波的定义、Spalart-Allmaras（SA）湍流模型和动态亚格子（subgrid-scale,SGS）模型关于湍流黏性系数的求解方式.理论分析结果表明,系综平均等价于盒式直接滤波,SAS和LES的控制方程在数学形式上具有一致性;SAS存在过多的湍流耗散,主要来自于SA输运方程中的扩散项.在数值模拟方面,选取来流Mach数0.55,Reynolds数2×105的圆柱可压缩绕流为分析算例.计算结果表明,SAS和LES预测的大尺度平均流场信息几乎一致,SAS预测的湍流脉动信息略低于LES.SAS在圆柱近尾迹区的湍流耗散过大,而在稍远的尾迹区几乎能够完全等效于LES.      

平流涡度方程及其在2006年Bilis台风分析中的应用

推导得到气压坐标中的动量叉乘形式的垂直涡度方程,这个动量叉乘形式的涡度方程包含了水平风的平流旋转效应,可称为平流涡度方程.由于水平风场的平流作用可由等压面天气图直观分析得到,因此平流涡度方程可方便用于实际天气分析.对2006年的Bilis台风移动过程中由经典涡度方程和平流涡度方程计算得到的垂直涡度倾向进行对比分析发现,二者计算得到的垂直涡度倾向变化的分布形式接近,但平流涡度方程计算得到的倾向的数值明显大于经典涡度方程的数值,正负涡度倾向区也更集中.对Bilis移动过程中的垂直涡度方程和平流涡度方程中各项的计算分析表明,水平风场的平流旋转作用是Bilis发展移动过程中垂直涡度变化的一个主要因素,是造成垂直涡度增强并发展的主要原因.因此,当水平风场平流旋转效应较强时,平流作用对垂直涡度倾向变化起主导作用,可直接用平流项来近似分析Bilis台风的涡度变化.而平流涡度方程中地转涡度和散度项的变化趋势与Bilis台风的移动路径有较好的一致性,这一项对台风的移动路径预报有更好的指示意义.     

解三维扩散方程的积分内插法格式

研究三维扩散方程的数值模拟.在非正规六面体网格上,使用积分内插法建立扩散方程差分格式,涉及到27个相邻网格,适用于大变形网格上带间断系数的拟线性扩散方程的计算.叙述差分格式的建立,推导通量流和网格顶点温度的计算公式,给出了数值试验结果.     

网格基任向偏导实现及层析应用

将光线偏折方程中的任向偏导转化为数值差分形式,并应用于层析线性运算.网格化待测场,将微分待测场的每一正方形网格及相应折射率近似为曲面底的正圆锥体,圆锥体顶端的折射率值对应该网格的折射率,在底面的投影对应网格的中心.假设紧邻三网格中心间的折射率分布共平面,在一个网格宽度内将偏导转化成数值差分形式.结果发现：基于上述近似和假设,可以将任意探测光线相关的偏导转化为数值差分形式,将非线性偏导方程转化为线性差分方程,建立层析方程.于是,偏折角可以作为投影直接重建.     

三能级Upper-ladder型系统中的

三能级Upper-ladder型系统中,在旋波、慢变振幅近似下,求解了考虑驱动场相位扩散后的系统密度矩阵运动方程,并给出了这个三能级梯型系统稳态线性解析解.利用对密度矩阵运动方程的稳态线性解析解的数值模拟结果,研究相位扩散对无反转激光增益、色散和粒子数差的影响;利用对密度矩阵运动方程的数值模拟结果,分析相位的扩散对无反...     

含分数阶微分的线性单自由度振子的动力学分析

研究了一个含分数阶微分的线性单自由度振子, 通过平均法得到了系统的近似解析解. 在近似解中, 分数阶微分项的系数和阶次以等效线性阻尼和等效线性刚度的形式影响着系统的动力学特性, 这一点与现有文献中直接将分数阶微分项归类为阻尼进行处理的方法完全不同. 比较了近似解析解和数值解, 二者的符合精度很高, 证明了近似解析解的准确性. 分析了分数阶系数和分数阶阶次对系统响应特性的影响, 发现分数阶系数和分数阶阶次都既可以通过等效线性阻尼影响系统的共振振幅, 又可以通过等效线性刚度影响系统的共振频率.     

求解Navier-Stokes方程组的组合紧致迎风格式

给出一种新的至少有四阶精度的组合紧致迎风(CCU)格式,该格式有较高的逼近解率,利用该组合迎风格式,提出一种新的适合于在交错网格系统下求解Navier-Stokes方程组的高精度紧致差分投影算法.用组合紧致迎风格式离散对流项,粘性项、压力梯度项以及压力Poisson方程均采用四阶对称型紧致差分格式逼近,算法的整体精度不低于四阶.通过对Taylor涡列、对流占优扩散问题和双周期双剪切层流动问题的计算表明,该算法适合于对复杂流体流动问题的数值模拟.     

A Schrödinger Potential Conditionally Integrable in Terms of the Hermite Functions

We introduce a biconfluent Heun potential well for the one-dimensional stationary Schrödinger equation which is composed of a confining fraction-power term and a repulsive centrifugal-barrier core. This is a conditionally integrable potential in that the strength of the centrifugal barrier is fixed to a constant. The potential supports a countable infinite number of bound states. We present the general solution of the Schrödinger equation, deduce the exact equation for the energy spectrumand derive a highly accurate approximation for energy levels. The bound state wave functions are written as irreducible linear combinations with constant coefficients of two Hermite functions of a scaled and shifted argument.

     

Modeling of filtered heat release for large eddy simulation of compressible infinitely fast reacting flows

A priori and a posteriori studies for large eddy simulation of the compressible turbulent infinitely fast reacting shear layer are presented. The filtered heat release appearing in the energy equation is unclosed and the accuracy of different models for the filtered scalar dissipation rate and the conditional filtered scalar dissipation rate of the mixture fraction in closing this term is analyzed. The effect of different closures of the subgrid transport of momentum, energy and scalars on the modeling of the filtered heat release via the resolved fields is also considered. Three explicit models of these subgrid fluxes are explored, each with an increasing level of reconstruction and all of them regularized by a Smagorinsky-type term. It is observed that a major part of the error in the prediction of the conditional filtered scalar dissipation comes from the unsatisfactory modeling of the filtered dissipation itself. The error can be substantial in the turbulent fluctuation (rms) of the dissipation fields. It is encouraging that all models give good predictions of the mean and rms density in a posteriori LES of this flow with realistic heat release corresponding to large density change. Although a posteriori results show a small sensitivity to subgrid modeling errors in the current problem, extinction–reignition phenomena involving finite-rate chemistry would demand more accurate modeling of the dissipation rates. A posteriori results also show that the resolved fields obtained with the approximate reconstruction using moments (ARM) agree better with the filtered direct numerical simulation since the level of reconstruction in the modeled subfilter fluxes is increased.     

Non-premixed turbulent combustion modeling based on the filtered turbulent flamelet equation

In turbulent combustion simulations, the flow structure at the unresolved scale level needs to be reasonably modeled. Following the idea of turbulent flamelet equation for the non-premixed flame case, which was derived based on the filtered governing equations(L. Wang, Combust. Flame 175, 259(2017)), the scalar dissipation term for tabulation can be directly computed from the resolved flowing quantities, instead of solving species transport equations. Therefore, the challenging source term closure for the scalar dissipation or any assumed probability density functions can be avoided;meanwhile the chemical sources are closed by scaling relations. The general principles are discussed in the context of large eddy simulation with case validation. The new model predictions of the bluff-body flame show sufficiently improved results, compared with these from the classic progress-variable approach.     

钛扩散铌酸锂矩形波导中的双折射耦合对传播常数的影响

 从亥姆霍兹方程出发，得到了各向异性光波导在弱导近似下的耦合模理论。耦合系数包括偏振耦合项和双折射耦合项。并用马卡提里近似下的模式作为零级近似。用一级微扰法计算了折射率渐变分布的钛扩散铌酸锂矩形波导的传播常数。在给定参数的情况下，得到双折射项引起的传播常数的改变约为主微扰项的3%，因此双折射耦合对钛扩散铌酸锂矩形波导的性能影响不可忽略，这对设计和分析与它相关的光波导器件具有指导意义。     

Cosmic chiral vortices

The review is devoted to cosmic chiral vortices (strings) and their possible role in the evolution of the early Universe. An exact cylindrically-symmetric solution to Einstein equations was obtained within the SU(2) sigma model for a configuration with a topological charge of the degree type. The linearized stability of the solution with respect to radial perturbations is proven by Lyapunov’s direct method. The metric found corresponds to the conical type with an angular deficiency proportional to the topological charge or the linear mass density of the vortex. The ray deflection angle close to the angular deficiency (the gravitational lens effect) was determined by direct integration of geodesic equations for the light ray orthogonal to the vortex. A gauge generalization of the model was considered involving the axially symmetric Yang-Mills field. In the approximation of the large topological charge, a solution with proper longitudinal magnetic field was obtained and the effect of a decrease in the vortex energy was found. The effect of closing the string was also considered in the approximation of the large closure radius. To this end, the toroidal moment of a closed string was calculated and an energy correction caused by the Skyrme term.     

Unstrained and strained flamelets for LES of premixed combustion

The unstrained and strained flamelet closures for filtered reaction rate in large eddy simulation (LES) of premixed flames are studied. The required sub-grid scale (SGS) PDF in these closures is presumed using the Beta function. The relative performances of these closures are assessed by comparing numerical results from large eddy simulations of piloted Bunsen flames of stoichiometric methane–air mixture with experimental measurements. The strained flamelets closure is observed to underestimate the burn rate and thus the reactive scalars mass fractions are under-predicted with an over-prediction of fuel mass fraction compared with the unstrained flamelet closure. The physical reasons for this relative behaviour are discussed. The results of unstrained flamelet closure compare well with experimental data. The SGS variance of the progress variable required for the presumed PDF is obtained by solving its transport equation. An order of magnitude analysis of this equation suggests that the commonly used algebraic model obtained by balancing source and sink in this transport equation does not hold. This algebraic model is shown to underestimate the SGS variance substantially and the implications of this variance model for the filtered reaction rate closures are highlighted.     

Fast prediction of scattered sound field based on Fourier diffraction theory under second-order born approximation

The directional pattern of sound waves scattered from an object insonified by a plane wave can be efficiently predicted using the Fourier diffraction theorem (FDT). This is achieved by sampling a circle in the discrete Fourier transform of the object/medium distribution. However, the FDT-based approach under the first-order Born approximation is only applicable to weak scattering. To improve the prediction accuracy and expand the method’s scope of applications, we introduce a second-order correction term to the solution, which is obtained by taking the first-order scattered waves as secondary incident sources, and calculate the “scattering” in the same way as in the first-order FDT-based approach. Adding the resulting correction term to the directional pattern based on the first-order Born approximation, the second-order prediction is obtained. Numerical results show that the proposed method can provide improved directional patterns of the scattered waves, and the range of applicability is significantly expanded.     

A priori analysis of subgrid scale pressure and heat flux in high pressure mixing and reacting shear layers

Direct Numerical Simulation (DNS) data on high pressure H₂/O₂ and H₂/air flames using the compressible flow formulation, detailed kinetics, a real fluid equation of state, and generalised diffusion are analysed. The DNS is filtered over a range of filter widths to provide exact terms in the Large Eddy Simulation (LES) governing equations, including unclosed terms. The filtered pressure and the filtered heat flux vector are extensively compared with the pressure and the heat flux vector calculated as a function of the filtered primitive variables (i.e. the exact LES term is compared with its form available within an actual LES). The difference between these forms defines the subgrid pressure and the subgrid heat flux vector. The analyses are done both globally across the entire flame, as well as by conditionally averaging over specific regions of the flame; including regions of large subgrid kinetic energy, subgrid scalar dissipation, subgrid temperature variance, flame temperature, etc. In this work, although negligible for purely mixing cases, the gradient of the subgrid pressure is shown to be of the same order as, and larger than, the corresponding divergence of the turbulent subgrid stresses for reacting cases. This is despite the fact that all species behave essentially as ideal gases for this flame and holds true even when the ideal gas law is used to calculate the pressure. The ratio of the subgrid pressure gradient to the subgrid stress tensor divergence is shown to increase with increasing Reynolds number. Both the subgrid heat flux vector and its divergence are found to be substantially larger in reacting flows in comparison with mixing due to the associated larger temperature gradients. However, the divergence of the subgrid heat flux vector tends to be significantly smaller than other unclosed terms in the energy equation with decreasing significance with increasing Reynolds number.     

Effect of the inertial term of the ion momentum equation on fluid transport simulation for capacitively coupled plasma sources

Fluid-based simulations are widely used to analyze or optimize capacitively coupled plasma sources. Although the inertial term of the ion momentum equation affects the accuracy of the solutions, the equation has not been considered in the drift-diffusion approximation model in the numerical solution. Therefore, we, herein, improved the accuracy of the model by applying an effective electric field, considering the inertial term. First, the effective electric field, including the ion inertial term of the ion momentum equation, was derived. Subsequently, one-dimensional fluid simulations were conducted. The numerical results were compared with those of one-dimensional particle-in-cell (PIC) simulations. The results of the developed model were similar to those obtained in the case of solving the full-ion momentum equation, as well as more similar to the PIC simulation results than those obtained in the case of the drift-diffusion approximation.     

The Fokker-Planck equation in the second-order pitch angle approximation and its exact solution

The diffusive particle propagation and its pitch angle scattering is studied using kinetic equation of the Fokker-Planck form. The case is considered when charged particles preferable propagate along the strong mean magnetic field direction and undergo the pitch angle scattering with respect to it. The paper deals with solution of the equation for particle distribution function in the second-order approximation in the pitch angle. The exact analytical solution is obtained in an integral form. The well-known solution in the first-order pitch angle approximation can be restored performing the small time limit in the result. Unlike the first-order solution the obtained solution in the second approximation rightly shows that the pitch angle diffusion is closely connected with the particle transport along the mean magnetic field. The expression for particle density for the point instantaneous unidirectional source also has been obtained.